521 ADV FLUID MECH II  
Winter 2003

                  
Hwk 3 (Due Mar 7)

1. Perform an experimental study showing the viscoelastic properties of a mixture of white glue and liquid starch ("silly putty"). Alternatively, you may choose another fluid.  You may wish to compare these to experiments with "more standard" liquids and solids.

2. Show for steady shear flow (u = gy) of a generalized Jeffrey Fluid that
      t_xy            = h₀g(1+l₁l₂g²)/(1+l₁²g²(1-a²))
      t_xx -t_yy  = 2h₀(l₁-l₂)g²/(1+l₁²g²(1-a²))
      t_yy -t_zz  = -h₀(l₁-l₂)g²/(1+l₁²g²(1-a²))      (pardon lack of dot over gamma.)

Find the unsteady t_xy  if a=l₂=0 (corotational Maxwell Model) and the flow starts from rest. A closed form solution is available when the deformation rate is small. Determine the force required to keep the plates separated at a constant value if the "wetted area" of the plate is A.

3. Find t_xx -t_yy for 2D steady elongational flow  (u = gx) for an upper-convected Maxwell model.
Hint: t_xx -t_yy  = 4h₀g  for 2D Newtonian and 3h₀g for axisymmetric Newtonian flow. If the tensile force F is constant, indicate how the length L of the sample increases with time.